# Re: Fw: Numbers

Russell,

Thats a good summary.  However, my issue with your conclusion is this:  even if I accept that a  "machine" or a "prime mover" is not necessary, such explanations are still part of the plenitude and therefore part of reality.  So if everything is reducible to math or information, even if you are correct that our reality can exist independent of these third-party explanations, such explanations still exist as part of the totality of everything that can exist.  What this would mean to me is that the reality I experience may occur naturally as a consequence of the logical bootstrapping you describe, but it would also be occuring through any number of artificial creations at the same time.  These realities overlap and it would be meaningless for me to try and say whether the reality I am experiencing now is one or the other- it is both.

If you accept MWI or the plenitude, there are really only a few ways to avoid the above argument.  First, you could argue that our reality is not reducible to computations or math or information, and therefore it is not possible to artificially create our reality.  Obviously, you and Marchal do not make this argument.  Second, you could argue that the creation of our universe requires some kind of infinite computation, and therefore the ability to artificially create it will forever lie beyond the means of intelligent beings.  However, I have always believed there are a number of problems with this argument, which I'll avoid right now.  Third, I guess you could argue that the reproduction of our universe to the point of emulation may require some kind of knowledge that would never be obtainable.  Again, if you accept that everything is reducible to math, then everything should be ultimately understandable at least in theory.

I may accept your bootstrapping argument, but the plenitude is going to also logically bootstrap other creations, such a Tiplers Omega Point, into existence which my reality is a subroutine of.  The fact is our reality is by and large pretty simple to describe.  I'm thinking we are a pretty run of the mill program in the plenitude...

Danny

Russell Standish wrote:
This is the way I put the argument in my upcoming book. You can also
read the Universal Dovetailer Argument in Bruno Marchal's SANE04
paper.

\item That a description logically capable of observing itself is
enough to bootstrap itself into existence. Let me speak to this by
means of an example: The C programming language is a popular
language for computer applications.  To convert a program written in
C into machine instructions that can execute on the computer, one
uses another program called a compiler. Many C compilers are
available, but a popular compiler is the GNU C compiler, or gcc. Gcc
is itself a C language program, you can download the program source
code from http://www.gnu.org, and compile it yourself, if you
already have a working C compiler. Once you have compiled gcc, you
can then use gcc to compile itself. Thus gcc has bootstrapped itself
onto your computer, and all references to any preexisting compiler
forgotten.

What I'm tryng to say here is that the description is a complete
specification of a conscious being, when interpreted (observed) by
the conscious being. There may have been an initial interpreter
(conscious or not) to bootstrap the original conscious being. It
matters not which interpreter it is --- any suitable one will do. If
{\em computationalism} \S\ref{computationalism} is correct, any
universal Turing machine will suffice. In fact since the 3rd person
world has to be a timeless {\em ideal} structure, it is not
necessary to actually run the initial interpreter. The logical
possibility of a conscious observer being able to instantiate itself
is sufficient in a timeless Plenitude of all possibilities. Thus we
close the ontology of the bitstring Plenitude, and find an answer
to Stephen Hawking's question What breathes fire into the
equations''\cite[p. 174]{Hawking88}. Paraphrasing the words of
Pierre-Simon Laplace to Napoleon Bonaparte, we have no need of a
hypothesis of a concrete reality\cite{Marchal98}.

I appreciate that some can never do this ontological closure, that for
them there must always be a machine somewhere doing the running. This
is reminiscient of those people for whom there must be a prime mover
to start the universe off.

I know that Bruno says he's eliminated the "extravagent hypothesis",
but really I think he's shown that it is unnecessary, and can be pared
away by Occam's razor, not that it is contradictory.

Cheers

On Sat, Mar 18, 2006 at 10:37:51PM -0800, Norman Samish wrote:

Are you saying that a tape of infinite length, with infinite digits, is not
Turing emulable?

I don't understand how the 'compiler theorem' makes a 'concrete' machine
unnecessary.  I agree that the tape can contain an encoding of the Turing
machine - as well as anything else that's describable.

Nevertheless, it seems to me there has to be a 'concrete' machine executing
the tape, irrespective of the contents of the tape.

Norman
~~~~~~~~~~~~~~~~~~~~~

----- Original Message -----
From: "Russell Standish" <[EMAIL PROTECTED]>
Sent: Friday, March 17, 2006 2:37 PM
Subject: Re: Fw: Numbers

But the tape can also hold an encoding of the Turing machine to perform the
interpretation. This is the essence of the "compiler theorem". One can
simply iterate this process such that there is no "concrete" machine
interpreting the tape. I think this is another way of putting the UDA.

Cheers

On Fri, Mar 17, 2006 at 01:31:22PM -0800, Norman Samish wrote:

[EMAIL PROTECTED] wrote:


"Hal Finney" wrote:
The first is that numbers are really far more complex than they seem.
When we think of numbers, we tend to think of simple ones, like 2, or 7.
But they are not really typical of numbers.  Even restricting ourselves
to
the integers, the information content of the "average" number is
enormous;
by some reasoning, infinite.  Most numbers are a lot bigger than 2 or 7!
They are big enough to hold all of the information in our whole
universe;
indeed, all of the information in virtually every possible variant of
our
universe.  A single number can (in some sense) hold this much
information.

How ? Surely this claim needs justification!
~~~~~~~~~~~~~~~~~~~~~
The single number can be of infinite length, with infinite digits, and can
therefore contain unlimited information.  One could compare the single
number to a tape to a Universal Turing Machine.  Granted, the UTM needs a
head and a program to read the tape, so the tape by itself is not
sufficient to hold information.

Norman
~~~~~~~~~~~~~~~~

    

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